Yenya's World

Tue, 21 Apr 2009

Statistics Problem

Is there any statistician reading this blog? Can you recommend any statistics
community (web forum, mailing list, anything) where I can ask questions about
one problem I am currently trying to solve? For those with login to
IS MU, the description will for some
time be also in the discussion forum of Faculty of Science. The problem is this:

I have a random variable with probability of exp(-a*t)
for some constant a and the time t (think radioactive decay,
but the real problem is something different). The problem is to calculate
the constant a from the observed data.

The measurements I have are in the form of a set of pairs
(ti, + or -), with the following meaning:
At time 0, take a brand new "i-th atom", verify that it is not decayed,
wait for the time ti, and look at it again. If the atom has
not decayed yet, add a (ti, +) pair to the set of
measurements. Otherwise, add (ti, -). Continue with the
next new atom an the next time ti+1.

Note however, that the times t_i are given to me from the outside,
I cannot choose them, and they do not have any particular distribution
(e.g. being equally distributed between time of zero and some large number).
Also, the number of measurements is quite small (several hundreds at most).

You can download a Perl script for generating the test data, the test data (100 rows),
and the large test data (10,000
rows)
generated by this script. Can you somehow compute which constants a
have been used when generating these sets of data? If so, how could it be
done? And how can I estimate how accurately the exp(-a*t) curve fits
the real data?